**1. Introduction**

In cellular organisms, DNA replication is a crucial and highly regulated process that follows specific steps, which vary slightly between prokaryotes and eukaryotes. In general, the earliest step in DNA replication is the establishment of replication origins, i.e., the genomic loci where DNA synthesis begins [1]. The start of replication is preceded by the binding of an initiator at the replication origins, which recruits and activates the replisome in a process called origin firing. Each origin fired produces two replication forks in opposite directions (bidirectional movement), which are responsible for synthesizing DNA at a rate that varies according to the organism and cell type [1–3]. The replication time required for all chromosomes determines the S-phase duration. Although the S-phase length is referred to as a way of regulating the cell cycle progression [4,5], recent studies have suggested that it is extremely robust [6–8].

Studies indicated that bacteria [1,9] and some protozoan parasites, such as *Leishmania* spp. [10], typically have one single origin per chromosome. On the other hand, most other eukaryotes, such as *S. cerevisiae* and *S. pombe*, generally have multiple origins per chromosome [9,11–13]. The exact number of origins per chromosome can vary according to cell type and the cellular environment [14]. However, the minimum number of origins (MO) required to duplicate an entire chromosome within

a specific S-phase duration must show minimal variation because it depends on two very constant factors: average replication rate and chromosome size [8].

In trypanosomatids, single-celled eukaryotes that encompass human pathogens are of great medical importance, and the question about how many origins are needed to replicate an entire chromosome during the S-phase is totally open [8,10,15,16]. Even for the widely studied domain Bacteria and the model eukaryote *S. cerevisiae*, this discussion is not yet a closed subject [1,17–19].

Here, we developed a website that is able to determine the duration of each cell cycle phase—G1, S, G2, mitosis (M), and cytokinesis (C)—in any organism. After using this website to obtain the S-phase duration for the organisms analyzed, we applied a formula developed by our group [8] and showed a comparative analysis between the minimum number of origins (MO) in trypanosomatids (*T. cruzi*, *L. major*, and *T. brucei*) and yeasts (*S. cerevisiae* and *S. pombe*). In addition to contributing to a discussion of why some organisms use far more origins than the minimum required, this study provides a clue about the dynamic of replication during the S-phase, raising questions about the possible phenomena involved in this process.

## **2. Materials and Methods**

#### *2.1. Trypanosomatids Culture, Growth Curves, and Morphological Patterns*

Epimastigote forms of *T. cruzi* (CL Brener strain) were cultured at 28 ◦C in liver infusion tryptose (LIT) medium supplemented with 10% (*v*/*v*) fetal bovine serum and 1% (*v*/*v*) antibiotic/antimycotic solution. Promastigote forms of *L. major* (strain Friedlin) were cultured at 26 ◦C in an M199 medium supplemented with 10% (*v*/*v*) heat-inactivated fetal calf serum, 25 mM HEPES, and 1% (*v*/*v*) antibiotic/antimycotic solution.

For the growth curves, each parasite culture was initiated with 1 × 10<sup>6</sup> cells.mL−<sup>1</sup> . Each growth curve was harvested and counted daily until it reached the stationary phase. For the establishment of the morphological patterns, formaldehyde-fixed and DAPI-stained exponentially growing parasites (*T. cruzi* and *L. major*) were examined under an Olympus BX51 fluorescent microscope (Olympus, Tokyo, Japan) (100× oil objective) to observe the profile of organelles that contain DNA (nucleus and kinetoplast).

## *2.2. EdU Incorporation Assays and 'Click' Chemistry Reaction*

Exponentially growing parasites were incubated with 100 µM 5-ethynyl-2′ -deoxyuridine (EdU) (ThermoFisher Scientific, Waltham, MA, USA) for the time required according to each assay at species-specific temperatures (28 ◦C for *T. cruzi* and 26 ◦C for *L. major*). The parasites were then harvested by centrifugation at 2500 *g* for 5 min, washed three times in 1× PBS (137 mM NaCl, 2.7 mM KCl, 10 mM Na2HPO4, and 2 mM KH2PO4, pH 7.4), and the pellet was resuspended in 200 µL of the same buffer solution. Afterward, 100 µL of the cell suspension was loaded onto poly-L-lysine-pretreated microscope slides (Tekdon, Myakka, FL, USA), fixed for 20 min using 4% sterile paraformaldehyde (Merck, Darmstadt, Germany) diluted in 1× PBS, washed three times with 1× PBS, and then washed three times with 3% BSA (Sigma-Aldrich, Saint Louis, MO, USA) diluted in 1× PBS. Then, parasites were permeabilized for 10 min with 0.1% sterile Triton X-100 (Sigma Aldrich, Saint Louis, MO, USA) diluted in 1× PBS, washed three times with 1× PBS, and then washed three times with 3% BSA in 1× PBS. To detect incorporated EdU, we used the Click-iT EdU detection solution for 45 min protected from light. The Click-iT EdU detection mix solution consisted of 25 µL 500 mM ascorbic acid (C6H8O6), 5 µL 100 mM copper sulfate (CuSO4), 2.5 µL Alexa fluor azide 488 (ThermoFisher Scientific, Waltham, MA, USA), and 467.5 µL distilled water (for details about EdU procedure, see ref. [20]). Finally, the parasites were washed five times with 1× PBS. Vectashield Mounting Medium (Vector, Burlingame, CA, USA) containing 4′ ,6-diamidino-2-phenylindole dihydrochloride (DAPI) was used as an antifade mounting solution and to stain nuclear and kinetoplast DNA. Images were acquired using an Olympus Bx51 fluorescent microscope (100× oil objective) attached to an EXFO Xcite series 120Q lamp and a digital

Olympus XM10 camera with camera controller software Olympus Cell F (Olympus, Tokyo, Japan). Images were further analyzed using ImageJ software (National Institutes of Health, USA) to count the numbers of EdU-positive parasites, and the percentage of proliferating parasites was calculated for each sample relative to the total number of DAPI-positive parasites.

## *2.3. Development of the CeCyD Website and Analysis of the Cell Cycle*

The website CeCyD (Cell Cycle Duration estimator) was developed using the Python programming language plus the Django v.1.8 framework. CeCyD is available at the following address http: //cecyd.vital.butantan.gov.br/, and its source code is released under the GNU GPL-3 license at https: //github.com/bruno-fs/CeCyD.

To estimate the duration of mitosis (M) and cytokinesis (C), the CeCyD uses the Williams (1971) equation [21]:

$$\alpha = \frac{\ln(1 - y/2)}{-a} \tag{1}$$

where *x* is the cumulative time within the cell cycle necessary to reach the start of the phase in question, i.e., the difference between the doubling time and *x* will give the time of the remaining phase(s); *y* is the cumulative proportion of cells up the phase in question (expressed as a fraction of one unit), i.e., the difference between the total cells (1% or 100%) and the percentage of cells in C or M+C, will provide the *y* value for C and M, respectively. Finally, α is the specific growth rate.

To estimate the G2 phase, the CeCyD must receive from the user the value corresponding to the period required for a cell to pass through G2 and M phases. For this, the user must apply an EdU pulse (e.g., 15 min) and then collected parasites every 15 min until a single cell containing two EdU-labeled nuclei (2N2K in case of trypanosomatids) is observed. The difference between this value and the duration of mitosis previously calculated corresponds to the G2-phase duration.

The S-phase duration is estimated by the CeCyD according to the Stanners and Till (1960) equation [22]:

$$S = \frac{1}{\alpha} \ln[L + e^{\alpha(Z)}] - (Z + t) \tag{2}$$

where *L* is the proportion of cells exhibiting EdU-labeled nuclei, α = ln 2/T (T = doubling time expressed in hours), *Z* = *G*2 + *M* + *C*, and *t* is the duration of the EdU labeling period in hours. Finally, the G1-phase duration is estimated by the difference between the doubling time and the sum of the remaining phases.
